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denis-greek [22]
3 years ago
12

A fish tank is a cube. Its side length is 4 1/2 feet. The volume of water needed to completely fill the fish tank is ___ cubic f

eet.
Mathematics
1 answer:
GalinKa [24]3 years ago
6 0

The equation for the volume of a cube is V=s^3, where V is volume and s is side length.  Plug in and solve:

V=4.5^3

V=4.5*4.5*4.5

V=91.125ft^3

Hope this helps!!

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Choose the expression that best represents the product of the width and the height
nexus9112 [7]
The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?

x best represents .

x + 12 best represents
6 0
2 years ago
Find the point on the parabola y^2 = 4x that is closest to the point (2, 8).
guapka [62]

Answer:

(4, 4)

Step-by-step explanation:

There are a couple of ways to go at this:

  1. Write an expression for the distance from a point on the parabola to the given point, then differentiate that and set the derivative to zero.
  2. Find the equation of a normal line to the parabola that goes through the given point.

1. The distance formula tells us for some point (x, y) on the parabola, the distance d satisfies ...

... d² = (x -2)² +(y -8)² . . . . . . . the y in this equation is a function of x

Differentiating with respect to x and setting dd/dx=0, we have ...

... 2d(dd/dx) = 0 = 2(x -2) +2(y -8)(dy/dx)

We can factor 2 from this to get

... 0 = x -2 +(y -8)(dy/dx)

Differentiating the parabola's equation, we find ...

... 2y(dy/dx) = 4

... dy/dx = 2/y

Substituting for x (=y²/4) and dy/dx into our derivative equation above, we get

... 0 = y²/4 -2 +(y -8)(2/y) = y²/4 -16/y

... 64 = y³ . . . . . . multiply by 4y, add 64

... 4 = y . . . . . . . . cube root

... y²/4 = 16/4 = x = 4

_____

2. The derivative above tells us the slope at point (x, y) on the parabola is ...

... dy/dx = 2/y

Then the slope of the normal line at that point is ...

... -1/(dy/dx) = -y/2

The normal line through the point (2, 8) will have equation (in point-slope form) ...

... y - 8 = (-y/2)(x -2)

Substituting for x using the equation of the parabola, we get

... y - 8 = (-y/2)(y²/4 -2)

Multiplying by 8 gives ...

... 8y -64 = -y³ +8y

... y³ = 64 . . . . subtract 8y, multiply by -1

... y = 4 . . . . . . cube root

... x = y²/4 = 4

The point on the parabola that is closest to the point (2, 8) is (4, 4).

4 0
3 years ago
Solve x3 = 64 over 27.
const2013 [10]

x^3 = 64/27

x^3 = (4*4*4)/(3*3*3)

x^3 = (4/3)^3

x = 4/3

ans is d


5 0
3 years ago
Read 2 more answers
Pleasd help me solve
krok68 [10]

Step-by-step explanation:

y = 2x

if x = 1 y = 2(1) = 2

if x = 2 y = 2(2) =4

4 0
2 years ago
Read 2 more answers
the length of a rectangle is 4cm longer than the width. the perimeter is 80cm. find the length and the width.
skelet666 [1.2K]

Answer:

I think it is 20cm

Step-by-step explanation:

divide 80 by 4 =20 cm

7 0
3 years ago
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